In the related art, it is known that a phenomenon called “creep” occurs in materials such as metals, polymers, and ceramics and that an object applied with a continuous load for long periods of time changes its size over time. Such a situation brings about various problems in a size-conscious industrial product. To prevent such problems, it is important to formulate and understand creep characteristics for each material at the time of designing the industrial product.
To describe a creep phenomenon with a formula, the following means is popularly practiced: that is, to use a definite relationship between increment of strain c and stress per unit time tin a constant creep range. A typical relationship is a power-law relationship between a minimum creep strain rate and stress, which is widely known as “power-law creep”, alias “Norton's law”, or “Dorn's law” (for example, Patent Literature 1).
                    [                  Mathematical          ⁢                                          ⁢          Formula          ⁢                                          ⁢          1                ]                                                                                  d            ⁢                                                  ⁢            ɛ                    dt                =                  k          ⁢                                          ⁢                      σ            n                                              (        1        )            
Herein, n represents a creep index, and k represents a creep constant, which are creep physical property values in a constant creep range.
As a constant load is applied to a test piece held under a predetermined testing temperature by a conventional testing standard for evaluating creep characteristics, for example, a test method prescribed in JIS-Z2271 (Metallic materials—Uniaxial creep testing in tension—Method of test), one strain rate can be evaluated. Therefore, in order to determine a creep index n and a creep constant k of the power law in Formula 1 based on a plurality of data points in which a strain rate and stress are considered as one set, it is required to conduct a plurality of tests. Herein, test conditions such as testing temperatures and applied stress change in several steps. Furthermore, one test requires several hours at minimum to several months at a maximum so that an immense amount of time and effort is required to complete the whole tests.
There is an indentation creep test method for evaluating creep physical property values easily and quickly (for example, Non-Patent Literature 1, and Patent Literature 2). Contact stress a generated by compressing an indenter on a surface of a test piece is defined by Formula 2 in which constant applied load P0 is divided by a time change Ac(t) of a projected contact area Ac of an indentation.
                    [                  Mathematical          ⁢                                          ⁢          Formula          ⁢                                          ⁢          2                ]                                                            σ        =                              P            0                                              A              c                        ⁡                          (              t              )                                                          (        2        )            
A contact area Ac(t), the denominator in Formula 2, cannot be measured by a typical indentation apparatus during load application. Therefore, the following method is widely prevalent. That is, an indentation depth h(t) is measured as an alternative to the contact area Ac(t), and the indentation depth h(t) is converted into the contact area Ac(t) by a reduction formula in Formula 3 which is a combination of functions representing a geometrical shape of an indenter and deformation behavior of a surface around an indentation.
                    [                  Mathematical          ⁢                                          ⁢          Formula          ⁢                                          ⁢          3                ]                                                                                  A            c                    ⁡                      (            t            )                          =                              g                                          γ                ⁡                                  (                  t                  )                                            2                                ·                                    h              ⁡                              (                t                )                                      2                                              (        3        )            
Herein, g is a constant determined by a shape of an indenter used in a test. For example, a value of g is 24.5 when using a Berkovich indenter having a three-sided pyramidal tip and an inclined face angle β of 24.7 degrees, as illustrated in FIG. 1, and when using a Vickers indenter having a four-sided pyramidal tip and an inclined face angle β of 22.0 degrees. Furthermore, γ(t) is a parameter of surface deformation representing behavior around an indentation on a surface of a test piece, and is defined by Formula 4 as a ratio of the whole indentation depth ht and a contact indentation depth hc as illustrated in FIG. 1.
                    [                  Mathematical          ⁢                                          ⁢          Formula          ⁢                                          ⁢          4                ]                                                                      γ          ⁡                      (            t            )                          =                              h            t                                h            c                                              (        4        )            
A value of γ(t) being 1 represents that a height around the indentation on the surface of the test piece is the same as the initial height before the test. A value of γ(t) being larger than 1 represents that a sink-in occurs in the surface around the indentation, while a value of γ(t) being smaller than 1 represents that a pile-up occurs in the surface around the indentation, which means that the surface around the indentation is higher than the initial height.
As can be seen from the theoretical formulae in Formula 2, Formula 3, and Formula 4, in order to measure creep stress in a quantitative way with a typical indentation creep testing apparatus, it is required to measure two parameters: a time change h(t) of the indentation depth and a time change γ(t) of the surface deformation around the indentation. However, a typical indentation creep testing apparatus in the related art cannot determine an in-situ quantity of a time change γ(t) of deformation of an indentation surface on a test piece during load application. Therefore, as an alternative to measuring γ(t) for each test, proximity using a theoretical solution (γ=π/2) of a conical indenter with respect to a perfect elastic body has been widely employed.
There is also know a method for optically observing and measuring a projected contact area Ac(t) of an indent generated as a measurement apparatus applies a load on a surface of a specimen (for example, Non-Patent Literature 2, Non-Patent Literature 3, Non-Patent Literature 4, Patent Literature 3, Patent Literature 4, and Patent Literature 5).